Certain Integral Transforms and Their Applications in Propagation of Laguerre-Gaussian Schell-model Beams

The principal aim of the present work is to investigate a new class of integral transforms involving the product of Bessel function of the first kind of arbitrary order with generalized Laguerre polynomials and logarithmic functions which deduce some new results in terms of the digamma function and Kampe de Feriet functions. A novel expression is found for the Kampe de Feriet function F-2:1;0(1:2;1) in terms of hypergeometric functions F-1(1) and F-2(2). Finally, the results obtained are applied in the problem of propagation of Laguerre-Bessel-Gaussian Schell-model beams as an application.

Automated summary

The principal aim of this work is to investigate a new class of integral transforms involving the product of Bessel functions and Laguerre polynomials, which leads to new results related to digamma functions and Kampe de Feriet functions. A novel expression for the Kampe de Feriet function is found in terms of hypergeometric functions. Finally, the obtained results are applied in the problem of propagation of Laguerre-Bessel-Gaussian Schell-model beams.